Dr Cosmic: Performing heroic acts on a supernatural power level does not have to be about punching bad guys all the time.
Saving millions of people, lifting buildings and heavy rocks, moving at great speed, interfering with the unbelievable forces of nature itself... shouldn't that be grand enough if it's approached in an epic way?
And a group of villains doesn't have to take too much of the screen time. If they have all been introduced before, just as the heroes were in their solo films, then we don't need to explore each of their back stories to explain who they are.
The answer to this is by using the most well-known villains: Lex Luthor, The Riddler etc
This is how I view the matters, anyway.
They can even use both the disasters and the villain league in the same film, making it connected in some way. Maybe having a main villain as the leader of the group gathering the other bad guys, and he/she should have found a plan to kill off people by changing the climate or control storms. I am not saying the villain should have a cube of great cosmic energy like Red Skull does, there can be other ways to alter our planet. But the first disaster can be followed by a chain of others, like a butterfly effect or something.